Odds of Getting In
There are plenty of psychology roles to choose from, and a nice bounty of jobs which will open up as soon as the previous generation retires (source). However, with tons of folks turning to this fascinating career, finding the training to get you there may be a struggle. Apply widely and keep your options open...you may have to travel to get your practice hours.
It helps to pick a school with good "match rates," meaning that many of its students find internships. When it comes time to look for a position, network with local and national professional organizations which can give you a boost.